if you have a pokemon that loses health, if it is regained with a potion WHLE IN BATTLE, does its happiness increase? If it is healed with multiple potions (if you're in a sandstorm, for example), will its happiness increase multpile times or only once? how does this affect the power of frustration and return in a battle with the miracle shooter?

realistically this only matters much for ingame tiers and miracle shooter but it's still important.

Actually, yes. BadIntent and I had a max attack Metagross using a double Helping Hand boosted Meteor Mash on max HP max defense Steelix, which did 93 damage. With one Helping Hand the damage range would be 60-71 (and normal damage would be 40-48).

if Intimidate lowers the attack of all the Pokemon in a Rotation Battle/Triple Battle? Even if it's not the active Pokemon in a rotation battle or if it's out of range for affecting a Pokemon in triples....

if Intimidate lowers the attack of all the Pokemon in a Rotation Battle/Triple Battle? Even if it's not the active Pokemon in a rotation battle or if it's out of range for affecting a Pokemon in triples....

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No. In rotation battles, intimidate only hits the pokemon in the front.

For Eccentric, when it says, "It transforms you into the enemy in front of you--i.e. your opponent," does that mean the pokemon with the ability will transform only into the pokemon directly in front of it (i.e. if you send a Ditto out into the left side of the field in a double battle, will it copy only the pokemon on the left side of your opponent's field) or is it random like Trace? If it does only copy the pokemon directly in front of Ditto, which pokemon will it copy if, in a Triple battle, it is switched in on a U-Turn/Volt Change by the middle pokemon that results in the opposing middle pokemon's fainting given that there are still pokemon on the left and right?